Editing General Relativity (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Calculating the Schwarzschild Radius and Gravitational Time Dilation:'''
<syntaxhighlight lang="python">
def calculate_schwarzschild_radius(mass_kg):
    """Returns the Schwarzschild radius in meters."""
    G = 6.67430e-11  # Gravitational constant
    c = 299792458    # Speed of light
    return (2 * G * mass_kg) / (c**2)

def gravitational_time_dilation(mass_kg, radius_m, time_interval):
    """
    Calculates time experienced by an observer at radius_m 
    compared to an observer at infinity.
    """
    rs = calculate_schwarzschild_radius(mass_kg)
    # Factor: sqrt(1 - rs/r)
    dilation_factor = (1 - rs / radius_m)**0.5
    return time_interval * dilation_factor

# Earth Example
earth_mass = 5.972e24
earth_radius = 6.371e6
rs_earth = calculate_schwarzschild_radius(earth_mass)
print(f"Earth's Schwarzschild Radius: {rs_earth:.5f} meters")

# Time dilation on Earth's surface for 1 second
dilated_sec = gravitational_time_dilation(earth_mass, earth_radius, 1.0)
difference_ns = (1.0 - dilated_sec) * 1e9
print(f"Time dilation at Earth's surface: {difference_ns:.5f} nanoseconds slower per second")
</syntaxhighlight>

; GR in the Modern World
: '''GPS''' → Crucial relativistic corrections for both velocity and gravity.
: '''LIGO''' → Detection of gravitational waves from colliding black holes.
: '''Event Horizon Telescope''' → Imaging the shadow of supermassive black holes (M87'', Sgr A'').
: '''Cosmology''' → Understanding the Big Bang and the accelerated expansion of the universe.
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